<h2>题目编号 : 133</h2>
<div style="color:#666;font-size:80%;">01 December 2006</div><br />
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<p>A number consisting entirely of ones is called a repunit. We shall define R(<var>k</var>) to be a repunit of length <var>k</var>; for example, R(6) = 111111.</p>
<p>Let us consider repunits of the form R(10<img src="" style="display:none;" alt="^(" /><sup><var>n</var></sup><img src="" style="display:none;" alt=")" />).</p>
<p>Although R(10), R(100), or R(1000) are not divisible by 17, R(10000) is divisible by 17. Yet there is no value of <var>n</var> for which R(10<img src="" style="display:none;" alt="^(" /><sup><var>n</var></sup><img src="" style="display:none;" alt=")" />) will divide by 19. In fact, it is remarkable that 11, 17, 41, and 73 are the only four primes below one-hundred that can <!-- ever--> be a factor of R(10<img src="" style="display:none;" alt="^(" /><sup><var>n</var></sup><img src="" style="display:none;" alt=")" />).</p>
<p>Find the sum of all the primes below one-hundred thousand that will never be a factor of R(10<img src="" style="display:none;" alt="^(" /><sup><var>n</var></sup><img src="" style="display:none;" alt=")" />).</p>

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